Is resolution and symmetry control in continuous free flow electrophores

ABSTRACT

IN A CONTINUOUS FREE FLOW ELECTROPHORESIS APPARATUS HAVING A THIN CURTAIN OF LIQUID CARRIER MEDIUM WHICH FLOWS ALONG THE LENGTH OF AN ELECTROPHORESIS SPACE BETWEEN A PAIR OF SPACED WALLS, THERE IS DISCLOSED A METHOD AND MEANS FOR ADJUSTING THE EFFECTIVE ZETA POTENITAL OF THE WALLS TO OPTIMIZE RESOLUTION AND TO COMPENSATE FOR ASYMMETRY OF THE CELL. RESOLUTION IS OPTIMIZED BY PROVIDING EACH OF THE WALLS OF THE APPARATUS WITH AREAS SPACED ALONG THE LENGTH THEREOF HAVING DIFFERENT ZETA POTENTIALS AND BY EITHER MECHANICALLY OR ELECTRICALLY ADJUSTING THE RELATIVE ELECTROOSMOTIC CONTRIBUTION OF EACH AREA. ASYMMETRY IS ELIMINATED BY MECHANICALLY OF ELECTRICALLY ADJUSTING THE ASYMMETRIES IN THE AREAS OF THE APPARATUS TO BE OPPOSITE IN SENSE TO EACH OTHER.

Sept. 11, 1973 $TR|KLER 3,758,395

RESOLUTION AND SYMMETRY CONTROL IN CONTINUOUS I FREE FLOW ELECTROPHORESIS Filed May 15, 1972 2 Sheets-Sheet 1 If! F 8 2 fia- Z V a;

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A. STRICKLER 3,758,395 RESOLUTION AND SYMMETRY CONTROL IN CONTINUOUS Sept. 1 1, 1973 FREE FLOW ELECTROPHORESIS 2 Sheets-Sheet 2 Filed May 15, 1972 p w w \lm w M 6 4 5 r4 6 7 7 w v i #1 I a 7 a 5 5 4, r f 2 ix 1 a fl r M M z (w ww w) [1 5, a Q Jfl fl W ?V Aw w 4... y m 5 6/. A a KW y m United States Patent 01 .a 5.... 1., 1.7.

3,758,395 RESOLUTION AND SYMMETRY CONTROL IN CONTINUOUS FREE FLOW ELECTROPHORESIS Allen Strickler, Fullerton, Calif., assignor to Beckman Instruments, Inc. Filed May 15, 1972, Ser. No. 253,290 Int. Cl. B01k 5/00 U.S. Cl. 204-180 R 22 Claims ABSTRACT OF THE DISCLOSURE In a continuous free flow electrophoresis apparatus having a thin curtain of liquid carrier medium which flows along the length of an electrophoresis space between a pair of spaced walls, there is disclosed a method and means for adjusting the effective zeta potential of the walls to optimize resolution and to compensate for asymmetry of the cell. Resolution is optimized by providing each of the walls of the apparatus with areas spaced along the length thereof having different zeta potentials and by either mechanically or electrically adjusting the relative electroosmotic contribution of each area. Asymmetry is eliminated by mechanically or electrically adjusting the asymmetries in the areas of the apparatus to be opposite in sense to each other.

BACKGROUND OF THE INVENTION (1) Field of the invention The present invention relates generally to continuous free flow electrophoresis apparatus and, more particularly, to a method and means for optimizing resolution and controlling asymmetry in a continuous free flow electrophoresis cell.

(2) Description of the prior art Electrophoresis, in general, is the phenomenon of migration of charged particles or ions in a liquid carrier medium under the influence of an electric field. This phenomenon can be used to fractionate mixtures of electrically charged small particles or ions into separate bands dependent on the electrophoretic mobility or surface properties of these components.

In one form of continuous electrophoresis applicable to particles or dissolved species, a buffer solution or electrolyte is caused to flow freely as a thin film or curtain in an electrophoresis space between a pair of substantially fiat plates of electrically insulating material mounted in substantially parallel, face-to-face relationship. The sample to be fractionated is injected continuously into the curtain in such a manner that it flows in a narrow band, entrained within the electrolyte. An electric potential gradient is applied to the curtain at some angle to the flow, typically being perpendicular thereto. Such potential gradient causes the lateral separation of the sample particles into various particle groups or components, in the form of a steady-state band pattern, depending upon many factors, including the electrophoretic mobility of the respective particles, the strength of the field, etc;

Many factors affect the performance of such continuous free flow electrophoresis cells. Factors such as the sample flow rate, the difference between the particle band zeta potential and the cell wall zeta potential, the location of the sample injection tip, and the electrical conductivity of the sample, especially in relation to the conductivity of the curtain, all affect the obtainable resolution. In my copending application Ser. No. 885,941, filed Dec. 17, 1969, now US .Pat. 3,663,395 ,for Cross- Section Illuminator for a Continuous Particle Electrophoresis Cell, substantial insight is given into the nature of liquid and particle movement in such a cell. More particularly, and as stated more fully therein, the vertical velocity profile of the electrolyte shows that there is a maximum velocity value at the center of the cell, which velocity diminishes in parabolic fashion to zero at the cell walls. With a DC electric potential gradient applied across the curtain, the vertical velocity pattern is unchanged, but there is now established a pattern of horizontal liquid movement. Such horizontal velocity pattern is also parabolic, but it has, in general, a finite velocity next to the walls rather than zero. In the midplane of the curtain, this movement is typically in a direction opposite to that of the walls. This is the pattern of electroosmotic flow in the cell, arising from the fact that the cell walls themselves are charged and have a definite zeta potential. Such velocity at the cell walls is proportional to the wall zeta potential. If the wall is negative and the anode is at the right, the liquid at the Wall moves to the left.

When a particle is introduced anywhere into the curtain, it will have two components of motion. Vertically, it will move essentially at the velocity of the liquid, this depending on the depth in the curtain in which it is entrained. Horizontally, the particle will have a certain velocity relative to the liquid, which is generally proportional to the zeta potential and the field gradient, this velocity being the same at any depth in the curtain. However, the observed horizontal velocity will be the sum of this electrophoretic velocity and the velocity of the liquid itself. The observed horizontal particle velocity, therefore, varies with depth, and in a parabolic manner.

As described in greater detail in my beforementioned copending application, if a stream of particles is introduced into the curtain, such stream having a generally circular cross-section, the deflectedband typically appears as a crescent in cross-section. This lateral spreading of the crescent is the main factor which inherently determines obtainable resolution in continuous free flow electrophoresis cells. It was also shown that the extent of lateral spreading of the crescent is critically dependent on the zeta potential of the cell walls relative to the sample zeta potentials. More specifically, resolution is an optimum when the electrophoretic velocity u of the sample component relative to the liquid is equal and opposite to the electroosmotic velocity u of the curtain liquid near the cell wall. Under this condition, the crescent-shaped band cross-section then reduces to a straight line, standing normal to the cell walls. As a result, nesting of closely spaced bands is eliminated and the resolution seen in any scanning technique is a maximum. Furthermore, selectivity in the collection of closely spaced fractions is greatly improved.

When the maxium resolution condition is not met, the observed bandwidth of the crescent increases in proportion to the algebraic sum of u+u It follows then that in a spectrum of particle bands, resolution is an optimum at one spectral position only and falls off to either side. However, since the range of zeta potentials in many particle mixtures is not large, a properly selected wall zeta potential, in many cases, gives a good working average of resolution. An incidential advantage of working near the resolution optimum is that sample flow may be increased several fold without serious resolution loss.

From the above discussion it will be apparent to those skilled in the art that the value of free film electrophoresis depends, in large measure, on the ability to modify or control the wall zeta potential. A number of Wall coating materials, spanning a sufficient zeta potential range, which are chemically stable, reasonably stable in zeta potential, and which can be applied or removed without solvent damage to the cell, have been suggested and successfully used. Examples of useful coating materials 3 are gelatin for low zeta potential samples, collodian for midrange zeta potential samples, and Mylar potential samples.

When selecting one of the above coatings to optimize the wall zeta potential, it is unnecessary actuallyto know the zeta potential of the coating or of the sample components. The reason for this is that the invention described and claimed in my beforementioned copending application functions to illuminate a section of the curtain, transverse to the curtain flow direction, so that the crescents may be readily observed. Such cross-section illuminator provides a valuable, practical tool for optimizing instrument performance in that it may be used to show the direction and amount of curvature of the crescentic band cross-sections, thereby acting as a null indicator. In other words, such cross-section illuminator may be used to show whether the wall zeta potential must be increased or decreased and approximately how much. The general rule is that if the convex side of the crescent faces the anode, the wall zeta potential must be made more positive and if it faces the cathode, the wall zeta potential must be made more negative.

While the coatings discussed previously have greatly improved resolution in many cases, they have, as a practical matter, been inadequate in solving the problem of optimizing cell resolution. In other words, many coatings, many coatings, closely spaced in zeta potential, would be needed to accommodate all samples to the best advantage. In addition, in order to adjust the wall zeta potential, openinng of the cell and discontinuance of the electrophoresis operation is required. Furthermore, such a procedure is simply not suitable for critical zeta potential adjustment directed at selected portions of a band sepctrum. Therefore, what has been needed is a technique giving an infinitely adjustable wall zeta potential. Preferably, such technique would not require opening of the cell to make the adjustment and would be applicable while the cell was in operation. However, heretofore, this has been unobtainable.

Finally, in my prior application, it was shown how cell asymmetry, due to a difference of zeta potential on the front and rear cell walls, distorts the crescent pattern, also limiting cell resolution. While the beforementioned coating techniques may be used to equalize the zeta potentials of the front and rear cell walls to eliminate cell asym-.

metry, no techniques have been available for making adjustments without opening the cell.

SUMMARY OF THE INVENTION In accordance with the present invention, there is disclosed a method and means for optimizing resolution and compensating for asymmetry in continuous free flow electrophoresis apparatus. With the present technique, the effective zeta potential of the cell walls is adjustable and it is not necessary to open the cell to make the adjustment. Resolution is optimized by providing each of the walls of the cell with areas spaced along the length thereof having different zeta potentials and by either mechanically or electrically adjusting the relative electroosmotic contribution of each area. For example, by varying the height ratio of the areas, any intermediate value of effective zeta potential can be obtained. Or, by individually adjusting the voltage gradient across each area, the same result can be achieved. In either event, rapid adjustment of the effective wall zeta potential may be achieved for maximum resolution with any type of sample. Furthermore, by simple variation of this concept, it is possible to also adjust the effective asymmetry of the cell. vMore specifically, an asymmetry in one portion of the cell can be compensated for by an asymmetry of opposite sense in another portion of the cell. This can be achieved by. varying the ratio of the field gradients or by varying the ratio of the zone heights.

It is therefore an object of the present invention to provide a technique for optimizing resolution in a continuous free flow electrophoresis cell.

for high zeta It is a further object of the present invention to provide a technique for controlling asymmetry in a continuous' free flow electrophoresis cell.

It is a still further object of the present invention to provide means for adjusting the effective zeta potential of the walls in a continuous free flow electrophoresis cell.

It is another object of the present invention to provide an electrophoresis cell having spaced zones having different zeta potentials and means for adjusting the relative electroosmoti c contributions of said zones.

Still other objects, features, and attendant advantages of the present invention will become apparent to those skilled in the art from a reading of the following detailed description of the preferred embodiments constructed in accordance therewith, taken in conjunction with the accompanying drawings wherein like numerals designate like parts in the several figures and wherein:

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a front sectional view of a portion of the inner face of one wall of a continuous free flow electrophoresis apparatus showing a two-zone coating thereon;

FIG. 2 is a schematic representation of the front and rear cell wall faces of a hypothetical continuous free flow electrophoresis cell;

FIG. 3 is a front elevation view of a continuous free flow electrophoresis cell constructed in accordance with the present invention;

FIG. 4 is an enlarged view taken along the line 4-4 in FIG. 3;

FIG. 5 is an enlarged view taken along the line 55 in FIG. 4; 7

FIG. 6 is aside sectional view of a portion of one wall of a continuous free flow electrophoresis cell according to another embodiment of the invention;

FIG. 7 is a front esectional view of a portion of the inner face of one wall of a continuous free flow electrophoresis cell showing still another embodiment of the present invention;

FIGS. 8 and 9 are schematic representations of portions of the inner faces of one wall of a hypothetical continuous free flow electrophoresis cell showing other embodiments of the invention; and

FIGS. .10 through 14 are schematic representations of DESCRIPTION OF THE PREFERRED EMBODIMENTS The present techniques for optimizing resolution and controlling asymmetry in a continuous free flow electrophoresis apparatus represent improvements in the field of electrophoresis and, therefore, the known apparatus for use therein will not be described in detail. For a more complete description of apparatus utilizing the phenomenon of electrophoresis, reference should be had to my US. Pat. No. 3,412,007, issued Nov. 19, 1968, for Continuous Flow Electrophoresis Apparatus or to US. Pat. No. 3,509,035, issued Apr. 28, 1970, to Victor H. Huebner for Continuous Particle Electrophoresis Cell and assigned to Beckman Instruments, Inc., the assignee of the present application. Accordingly, only so much of such electrophoresis cells as is necessary for an understanding of the present invention will be described hereinafter. Furthermore, although the flow direction will be assumed hereinafter to be vertical, it should be understood the cell plane could be horizontal and that all references herein to heights shall be construed to refer to the length in the longitudinal or flow direction.

It is the general teaching of the present invention that the effective zeta potential of the walls of an electrophoresis cell may be adjusted by providing a cell in which each of the front and rear inner surfaces, lying within the field zone, is a composite of at least two areas, With reference to FIG. 1, there is shown that portion of the inner surface of a cell wall lying within the field zone. Surface 5 is divided into an upper rectangular area A and a lower rectangular area B. Upper area A is coated With a material having a first zeta potential and lower area B is coated with a material having a different zeta potential value The arrangement of these areas and their zeta potentials is the same on the rear inner surface, not shown. If a given fractionation requires an effective wall zeta potential g' lying within the range 9, to 3,, this may be obtained, according to a first embodiment of the present invention, by adjusting the height H of area A relative to the height of H of area B. The effective wall zeta potential is the height-weighted average of the zeta potentials of areas A and B in accordance with the expression:

The effective electroosmotic boundary velocity adjacent to surface 5 may be defined by the expression:

u LwA A LWB B HA+HB Where u land u are the individual electroosmotic boundary velocities which are related to the respective wall zeta potentials by the familiar Helmholtz-Smoluchowski relationship:

where E is the electric field gradient, D is the dielectric constant of the medium, and 1; is the viscosity of the medium. In other Words, it can be shown mathematically that a sample particle passing between the front and rear surfaces at any relative depth in the cell thickness experiences a lateral displacement x equal to the sum of the partial displacements x and x experienced while passing areas A and B and that this total lateral displacement is equal to that for a uniformly coated cell in which the electroosmotic velocity u equals the heights-weighted average for the two zoned cell of FIG. 1.

In its simplest form, the present invention permits infinite adjustment, but requires opening of the cell. As an example of this approach, Mylar film substrates on the inner surfaces of the cell Walls may be coated throughout their lengths with collodian, giving one zeta potential value, then overcoated along a portion of the length with gelatin, giving a much different zeta potential value. If the height of the gelatin zone is initially insufficient for the desired effective zeta potential, this may be increased by successive trial steps, by enlarging the height of the gelatin coated portion.

In order to avoid opening the cell, one could use a coating of amphoteric material or two coatings having different isoelectric points. Moderate adjustment of the pH of the medium would then alter the single zeta potential or the relative zeta potentials of the coatings and therefore the effective or overall wall zeta potential value. Of course, the sample being fractionated would have to tolerate the necessary pH changes. Another requirement is that the mobility of the components of interest not change with pH at the same rate and in the same direction as the effective u value. The advantage of two such coatings as compared with a single coating is that the required effective wall zeta potential may be attained at a pH more compatible with sample integrity.

Another way to avoid opening the cell is to draw a liquid into it from below, partially filling the cell. The liquid may then dissolve off a coating from the walls to some desired level or, it may deposit a coating or cause some chemical change. Magnetic or thermal effects, locally applied, could also alter the physical-chemical surface properties, thereby altering the zeta potential.

The ideal control would permit varying the effective wall zeta potential value without interrupting the electrophoresis operation. One could then literally focus the system for optimum resolution at any desired band position while observing the crescent patterns with the crosssection illuminator of my beforementioned copending application. Some of the approaches suggested above could be amenable to such control. However, the result may also be achieved directly by mechanical or electrical means, as described hereinafter.

Referring now to FIG. 2, lines 6 and 7 represent the inner wall faces, seen in vertical section, of a conventional electrophoresis cell 4. The upper halves of the wall faces, from C to G and from E to H are of one zeta potential value, and the lower halves of the cell wall faces, from G to D and from H to F are of another zeta potential value, Lines 8 and 9 represent slides or masking elements, each of about half the field zone height, lying in near contact with cell faces 6 and 7, respectively. Such slides or masking elements 8 and 9 are adapted for simultaneous vertical movement to cover any desired position along the wall faces from C to D and from E to F. The inner surfaces of slides 8 and 9, facing the curtain midplane, would be of equal zeta potential value, either approximately the zeta potential value of zones CG and EH or that of zones GD and HF. If, for example, the zeta potential of masks 8 and 9 were the same as that of surfaces CG and EH, movement of masks II and KL upwardly through the full range of the field space would then vary the effective cell zeta potential from f to Referring now to FIGS. 3 through 5, there shown an electrophoresis cell, generally designated 10, including a gasket 11 between a pair of cell plates 12 and 13, gasket 11 defining an electrophoresis space 14. Cell 10 includes cathode and anode chambers which are each shown as divided into two parts 15, 16 and 17, 18, respectively, leaving an intermediate space to accommodate drive wheels 20 and 21 which lie in rear plate 12 and drive wheels 22 and 23 which lie in front plate 13.

According to the present invention, electrophoresis apparatus 10 includes a pair of masks 25a and 25b which are positioned parallel to and in contact with the faces of plates 12 and 13. Typically, masks 25a and 25b would be thin sheets of a polymer such as Mylar having high dimensional stability under continuous immersion in water or buffer. The inner faces of masks 25a and 25b and cell surfaces 12 and 13 are suitably coated, as described previously.

The edges of masks 25a and 25b are lined with perforations 26 which are engaged by toothed wheels 20-23. More specifically, drive wheels 20 and 21 may be mounted on a common shaft 27 which extends through rear plate 12 and has one end lying externally thereof and connected to a hand wheel 28. Similarly, drive wheels 22 and 23 may be mounted on a common shaft 29 which extends through front plate 13 and has one end lying externally thereof and connected to a hand wheel 30. Wheels 20-23 may be positioned in recessed wells 31 and 32 in plates 12 and 13, respectively, the teeth on wheels 20-23 extending beyond the inner surfaces of plates 12 and 13. Masks 25a and 25b are positioned in contact with the inner surfaces of plates 12 and 13, respectively, and may be retained by a shoulder in cell gasket 11, which serves as a guide or track. The spacing between the rows of perforations 26 in masks 25a and 25b is such that the teeth on wheels 20 and 21 engage perforations 26 in mask 25a and the teeth on wheels 22 and 23 engage perforations 26 in mask 25b. Perforations 26, at the same time, provide for ionic continuity between the electrode chambers and the curtain space.

In operation, rotation of hand wheels 28 and 30 operates to shift masks 25a and 25b vertically within electrophoresis space 14 making the effective wall zeta potentials infinitely adjustable between two values, as discussed previously with respect to the generalized structure shown in FIG. 2.

In the embodiment of FIGS. 35 with any two cell surface materials of different zeta potentials, one may derive a span of working zeta potentials equal to half the span defined by the different surface materials. On the other hand, one may device other physical arrangements giving the full span of working zeta potentials between the limits set by the different materials.

More specifically, and with reference to FIG. 6, there is shown a portion of an electrophoresis cell, namely a single cell plate 40, having a pair of drums 41 and 42 mounted therein around which extends a continuous flexible belt 43. Such a continuous flexible belt would be mounted in each cell plate and made externally rotatable such as in the manner shown with respect to FIGS. 35. A pair of idler drums 44 and 45 may also be mounted in cell wall 40 to control the path of movement of belt 43. In any event, belt 43 may have two coating zones, positioned end to end, which would be of different zeta potentials, and the length of each zone would be at least equal to the height of the field zone. Rotating the two drums would bring any desired height ratio of the two different surfaces into the electrophoresis cell giving the full span of working zeta potentials between the limits defined by the two coating zones.

With any of the embodiments of FIGS. 2-6, only one band of a particle spectrum would have optimum resolution. In other words, in a spectrum of particle bands, resolution is an optimum at one spectral position only and falls off to either side. However, since the range of zeta potentials in many particle mixtures is not large, a properly selected wall zeta potential, in many cases, gives a good working average of resolution. Moreover, if high resolution is desired over an increased range of particle velocities, but maximum sample rate is not essential, this can be achieved by reducing the sample flow such that the sample stream occupies a smaller fraction of the curtain thickness.

Referring now to FIG. 7, theer is shown a technique whereby all of the bands of a particle spectrum may simultaneously be at optimum resolution. Furthermore, the embodiment of FIG. 7 requires no mechanical moving parts. More specifically, there is shown a portion of one wall 50, taken through the curtain midplane, showing the field zone divided into two areas and P separated by a line QR. Wall area 0, above dividing line QR, is coated for one zeta potential value whereas wall area P, below line QR, is coated for another zeta potential value. It should be noted that dividing line QR is canted with respect to the sample flow band lines 51 so that components deflected at different angles have different ratios of transit times in the two zones. If the line QR is properly drawn, each component band can be made to traverse a path for which the effective electroosmotic velocity u adjacent to the wall, is equal and opposite to the band mobility u. The equation of the curve meeting these conditions is:

LWP g nwo) ie-g Lwo where x equals the lateral displacement at the bottom of zone P, y equals the vertical liquid velocity at middepth, u and u are the electroosmotic velocities adjacent to the walls of the upper and lower zones 0 and P, respectively, H is the field height, and H is the height of the curve above the field base line at any lateral position x. It will be observed that the curve is parabolic, with an axis normal to the curtain fiow direction. Preferably, zones 0 and P should differ enough in zeta potential to give a range considerably exceeding the sample zeta potential range. Otherwise, curve OR may be very steep in slope and may disturb the particles by shifting them in depth at the crossover point.

One limitation of such an approach is that it cannot readily be adjusted if a shift occurs in the wall zeta potentials. Also, a given boundary curve is valid only at a predetermined voltage gradient and for the zeta potentials of wall and sample prevailing in a given curtain medium.

In the preceding, it has been shown that resolution may be optimized by adjusting the effective zeta potentials of the walls by providing the walls with two spaced zones having different zeta potentials, and by varying the height ratio of said zones. However, the present invention teaches that such tuning of the effective zeta potential may be achieved also by purely electrical means. This possibility arises from the fact that in a dual zone arrangement, the voltage gradient across each zone plays the same role, quantitatively, as the zone height in determining the relative electroosmotic contribution of each zone. Thus, for example, the two zones may be kept equal in height and the ratio of the voltage gradients applied across them may be varied.

Referring now to FIG. 8, there is shown, schematically, a cell wall 55 having an upper area A flanked by its own pair of electrode slots S and electrode pair e and a lower area B, of different zeta potential, flanked by its own pair of electrode slots 8;; and electrode pair The arrangement of coatings A and B is the same on the rear inner cell surfaces, not shown. Assuming the heights of areas A and B are equal, the effective cell zeta potential will be the average of the zeta potentials provided by areas A and B weighted by the respective applied voltage gradients. If the two area heights are different, the zeta potentials are weighted by the product of area height and voltage gradient.

The theoretical basis for this proposition follows from the general particle displacement equation:

1/0 1-2 Y 5) which applies for any zone of uniform zeta potential in a free-film electrophoresis cell, where H is the field height, y is the vertical midplane velocity of the curtain, lu is the electrophoretic particle velocity, u is the electroosmotic velocity of the liquid adjacent to the walls, and z is the relative particle depth in the curtain, defined as +1 at the rear walls, 0 at the midplane, and 1 at the front wall. By substituting for u and u respectively, the products E11 and Ev where E is the field gradient, 11 is the particle mobility, and v w is the liquid mobility adjacent to the walls, Equation 5 is modified to:

EH 11+1 w ya. 1-z 2 It should be noted from Equation 6 that both E and H operate in an analogous manner in the equation, indicating that either or both may be altered to vary the electroosmotic contribution of either coating zone.

Referring again to FIG. 8, the displacement function will be the sum of the displacements for the two zones in accordance with the equation:

This is equivalent to the displacement function of a cell with a single coating and a single electrode pair in which the height is taken as H +H the voltage gradient is taken as the zone height-weighted average of E and E and the liquid mobility adjacent to the wall is taken as the average of VLWA and v weighted by their respective products B H, and E H i.e.

EAHAVLWA +EBHBVLWB E H +E H For such hypothetical cell, if the displacement function were to be written out in the form of Equation 6 and then reduced and rearranged, it would be shown to be the same as Equation 7 providing the equivalence of the hypothetical single zone cell and the dual zone cell. Such equivalence has also been proven by actual experiment. Given then a portion of a particle spectrum in which resolution is to be optimized, the particle mobility in that zone being 11, and given the characteristic v and VLWB values of the two coating materials in the given medium, and adjustment is made of the ratio of the height-gradient product, EH, of the zones such that the effective v value of the total cell is 1 or Dividing through the enumerator and denominator on the left side of Equation 9 by E H and solving for the required product ratio, we derive In practice, of course, H and H are fixed in the embodiment shown in FIG. 8 and the ratio E /E is varied empirically until optimum resolution is observed visually with the cross-section illuminator of my beforementioned copending application. n the other hand, if we make E equal to B and vary the ratio of H to H we have the embodiments of FIGS. 1 through 7.

With a cell configuration as shown in FIG. 8, there will be a slight cross-effect between electrode pairs e and e;;. For example, when no field is applied to electrodes :2 a small fraction of the field gradient from electrodes 2;, will appear across zone B and vice versa. The extent of cross-effect depends on the gap size between the upper and lower electrodes as well as on details of cell design in the vicinity of the electrode chambers and slots. When the gap-to-lateral spacing ratio is 1:5, for example, the crossover is a maximum of about 13%, which is not objectionable. It merely means that the effective ratio of the field gradients on the two zones will always be slightly less than the actual ratio of the applied voltages.

Referring now to FIG. 9, there is shown a modification to the embodiment of FIG. 8 wherein a pair of sliding covers 60 and 61 are movable vertically on the surface of, or within slots S and S to block a variable portion of the field from the electrophoresis zone. Again here, the two coated zones are fixed in height and position in the cell and the applied voltage from electrodes 2.; and e is fixed. However, by moving covers 60 and 61, the field limits are vertically shifted by a mechanical arrangement so as to include within the field a variable ratio of coating heights. By actuating covers 60 and 61 together from outside of the cell by some suitable means, adjustment of the relative electroosmotic contribution of each zone may be achieved. In the position shown, only heights H and H of zones A and B, respectively, are electroosmotically active. The ratio of these heights is altered by raising or lowering covers 60 and 61, permitting adjustment of the effective wall zeta potential and the resolution.

In all of the structures discussed above, the portions of the inner cell surfaces facing each other were assumed to be of equal zeta potential and u value. Actually, this is not a necessary condition, as can be demonstrated from the theory of the asymmetrical cell. Referring now to FIG. 10, there is shown a schematic surface diagram for an asymmetrical, segmented cell 65 including a front surface F and rear surface R. Front surface F is composed of two zones UV and VW having zeta potentials Q11 and K respectively. Rear surface R is composed of two zones XY and YZ having zeta potentials and f respectively. It may be readily shown that the behavior of the combined cell length is the same as if surfaces F and R were each of uniform zeta potential along their full lengths, with front surface F having a zeta potential equal to the height-weighted average of and .1 and with rear surface R having a zeta potential equal to the height-weighted average of and Extension of the principal shows that so long as surfaces F and R each have a certain height-weighted average of zeta potential, the vertical distribution of the zeta potential is immaterial. The segments on each face may be of any arbitrary number and of different heights on the two faces, and

, the variations may be continuous. If therefore follows also that if the vertically averaged potentials on surfaces F and R are equal and of an effective u equal t0:u for a given sample component, then resolution will be a maximum at the spectral position of that component, regardless of the vertical zeta potential distribution on either cell face.

Accordingly, the present invention teaches how, by a simple variation of the electrical resolution control concept discussed with reference to FIGS. 8 and 9, it is possible also to adjust the effective asymmetry of a cell. That is, if for any reason the effective zeta potential on the front cell face differs from that on the rear cell face, causing abnormal band broadening, it is possible to introduce a compensating asymmetry to eliminate the overall asymmetry in the observed crescent pattern. In this manner, resolution can be optimized and maximum band sharpness obtained despite drift or variation in surface potentials which introduces an asymmetric condition.

Referring now to FIG. 11, there is shown schematically the front and rear cell faces F and R of a hypothetical cell 70. Front cell face F is divided into zones a and c which have unequal heights H and H respectively, and different zeta potentials and i Rear cell face R includes zones b and d of unequal heights H and H respectively, and different zeta potentials 5' and While zones a and b are of equal height, they may have different zeta potentials. Furthermore, zones c and d are of equal height but may differ in height from zones a and b and may differ from each other and from zones a and b in zeta potential. The voltage gradients across zones 11, b and c, d are E and E respectively, and are, of course, applied to cell 70 perpendicular to the plane of FIG. 11.

If a generalized particle displacement function for the composite cell 70 is derived, it can be shown mathematically and experimentally to be equal to the particle displacement function for a cell in which each of the front and rear faces has a uniform v value equal to the average of the separate v values weighted respectively by the gradient-height products of the zones and in which a uniform voltage gradient E is applied, equal to the Zone height-weighted average of E and E As a simple example, reference is made to FIG. 12 which shows schematically a cell 71 including front and rear faces F and R each divided into upper and lower zones in which H equals H and in which the coating materials a is the same at the top front and lower rear zones and the coating material b is the same at the top rear and lower front zones. Again, the applied field gradients across the upper and lower zones are E and E respectively. In the case of FIG. 12, the relative electroosmotic contributions of the upper and lower zones may be varied by varying the ratio of E to E If no field is applied to the lower zones, the crescent pattern shows simply the asymmetry due to the different a and b coatings of the upper zones only. Similarly, if no field is applied to the upper zones, the crescent pattern shows simply the asymmetry due to the different a and b coatings of the lower zones only, the observed pattern asymmetry being reversed, front-to-back, from that observed previously. If an equal voltage gradient E is applied to the upper and lower zones, and if the general equation for particle displacement is calculated, we obtain a result which may be expressed in the form This is the crescent equation for a symmetrical cell in which both the front and rear walls have the same zeta potential, equal to the average of the zeta potentials of zone coatings a and b.

In other words, it is the teaching of the present invention that an asymmetry in one portion of a cell, such as cells 70 and 71, can be compensated for by an asymme try of opposed sense in another portion of the cell. In the example shown in FIGS. 11 and 12, the ratio of the field gradients has been varied. The ratio of the zone heights could equally well be varied so that a method corresponding geometrically to that of FIG. 9 could be used, or to that of FIGS. 3-6.

Referring now to FIG. 13, there is shown schematically the front and rear cell faces F and R of a hypothetical cell 72. In cell 72, cell faces F and R are each divided into three vertically spaced segments. The upper zones comprise a major portion of the field zone and have a main coating 1 on both front and rear surfaces. The lower two zones on both faces comprise a lesser portion of the cell height and have coatings g and h for asymmetry correction. More specifically, the coating material g is the same at the central front and lower rear zones and the coating material It is the same at the central rear and lower front zones. If the upper zones become asymmetrical due to differential surface contamination or for any other reason, the ratio of the supplementary voltages E and E applied to the lower two zones can be altered to compensate for the asymmetry.

Referring now to FIG. 14, an alternative arrangement is shown in which adjustment for band curvature and asymmetry may both be built into the same cell. FIG. 14 shows the front and rear cell faces F and R ofa hypothetical cell 73, each of which is divided into four zones having four electrode pairs. More specifically, front cell face F is divided into zones 75-78 and rear cell face R is divided into zones 8588, zones 75 and 85 having equal heights, zones 76 and 86 having equal heights, zones 77 and 87 having equal heights, and zones 78 and 88 having equal heights. Voltage gradients equal to E E E and B are applied across zones 75, 85, 76, 86, 77, 87, and 78, 88, respectively. Finally, zones 75, 78, 85, and 87 have a coating m of one zeta potential value whereas zones 76, 77, 86, and 88 have a coating n of another zeta potential value.

The upper two pairs of zones provide resolution control by adjustment of the ratio of E to E On the other hand, the lower two pairs of zones employ the same coatings, but in opposed asymmetric arrangement, to provide asymmetry control by adjustment of the ratio E to E A somewhat simpler arrangement for dual resolutionasymmetry control would be the FIG. 13 configuration in which the average zeta potential of coatings g and h would be either appreciably greater or less than the zeta potential of coatings 1. For the condition in which no asymmetry correction is desired, E and E would be equal, but the ratio of the E E voltage to the E voltage would be varied for control of resolution. For correction of asymmetry only, E would be held constant and the ratio of E to E would be varied while maintaining their the present technique, the effective zeta potential of thecell walls is adjustable and it is not necessary to open the cell to make th adjustment or even to interrupt the continuous separation process. Resolution is optimized by providing each of the walls of the cell with spaced areas having different zeta potentials and by either mechanically or electrically adjusting the relative electroosmotic con: tribution of each area. For example, by varying the height ratio of the areas, any intermediate value of effective zeta potential can be obtained. Or, by individually adjusting the voltage gradient across each area, the same result can be achieved. In either event, rapid adjustment of the effective wall zeta potential may be achieved for maximum resolution with any type of sample.

Furthermore, by a simple variation of this same concept, it is possible to also adjust the effective asymmetry of the cell. More specifically, an asymmetry in one portion of the cell can be compensated for by an asymmetry of opposite sense in another portion of the cell. This can be achieved by varying the ratio of the field gradients or by varying the ratio of the zone heights.

While the invention has been described with respect to the preferred physical embodiments constructed in accordance therewith, it will be apparent to those skilled in the art that various modifications and improvements may be made without departing from the scope and the spirit of the invention. Accordingly, it is to be understood that the invention is not to be limited by the specific illustrative embodiments, but only by the scope of the appended claims.

I claim:

1. In a continuous free flow electrophoresis apparatus having a thin curtain of liquid carrier medium which flows along the length of an electrophoresis space between a pair of spaced walls, the improvement wherein each of said walls is composed of areas spaced along said length having different zeta potentials and comprising means for adjusting the relative electroosmotic contribution of said areas.

2. In a continuous free flow electrophoresis apparatus according to claim 1, the improvement wherein said ad 4. In a continuous free flow electrophoresis apparatus according to claim 3, the improvement wherein each of said areas is equal in height, wherein each of said masking elements has a height approximately equal to the height of said areas, and wherein the zeta potentials of said masking elements are equal to each other and to that of one of said areas. 7

5. In a continuous free flow electrophoresis apparatusaccording to claim 4, the improvement wherein each of said masks has first and second rows of perforations on.

opposite lateral sides thereof and wherein said means for moving said masks longitudinally comprises drive .wheels mounted within said walls, said drive wheels engaging said perforations in said masks, said drive wheels being mounted on shafts extending through said wallsand terminating externally thereof for manual manipulation.

6. In a continuous free flow electrophoresis apparatus,

according to claim 2, the improvementcomprising a pair of drums mounted within each of said walls and. a con-,

tinuous flexible belt extending around each of said pairs of drums, said continuous flexible belt having two areas.

of different zeta potentials, positioned end to end, the

length of each area being at least equal to the height'of v the field applied across said electrophoresis space.

7. In a continuous free flow electrophoresis apparatus I:

according to claim 6, the improvement wherein said height ad usting means comprises means for rotatin one of said 13 drums thereby rotating said continuous belt to bring any desired height-ratio of said two different areas into said electrophoresis space.

8. In a continuous free flow electrophoresis apparatus according to claim 2, the improvement wherein an electric field is applied across each of said areas and wherein said height adjusting means comprises means for shifting the height of the field applied across one of said areas relative to that applied across the other of said areas.

9. In a continuous free flow electrophoresis apparatus according to claim 1, the improvement wherein said adjusting means comprises means for adjusting the voltage gradient across one area relative to the other.

10. In a continuous free flow electrophoresis apparatus according to claim 1 wherein the zeta potentials of the areas at one position along said spaced walls are asymmetrical, the improvement wherein said adjusting means comprises means for adjusting the asymmetry of the areas at a different position along said walls to be equal to and opposite in sense to the asymmetry of said areas at said one position.

11. In a continuous free flow electrophoresis apparatus according to claim 10, the improvement wherein said asymmetry adjusting means comprises means for providing said areas at said different position with different zeta potentials which are opposite in sense to the dilference in zeta potentials of said areas at said one position and means for adjusting the voltage gradient across the areas at said difierent position relative to that across the areas at said one position.

12. In a continuous free flow electrophoresis apparatus having a thin curtain of liquid carried medium which flows along the length of an electrophoresis space between a pair of spaced walls, a method for adjusting the etfective zeta potential of said walls comprising:

dividing said wallls into two, longitudinally spaced areas having ditferent zeta potentials; and

adjusting the relative electroosmotic contributions of said areas.

13. A method according to claim 12 wherein said step of adjusting the relative electroosmotic contributions of said areas comprises: adjusting the effective height of one of said areas relative to the height of the other of said areas.

14. A method according to claim 13 further comprising the step of applying an electric field across each of said areas, and wherein said step of adjusting the relative electroosmotic contributions of said area comprises: altering the height of the field applied across one of said areas relative to that applied across the other of said areas.

15. A method according to claim 12 wherein said longitudinally spaced areas are coated with amphoteric materials having difierent isoelectric points and wherein said step of adjusting the relative electroosmotic contributions of said areas comprises: adjusting the pH of said carrier medium.

16. A method according to claim 12 wherein said step of adjusting the relative electroosmotic contributions of said areas comprises: adjusting the dividing line between said areas to be parabolic with an axis normal to the curtain flow direction.

17. A method according to claim 12 wherein said step of adjusting the relative electroosmotic contributions of said areas comprises: adjusting the voltage gradient across one of said areas relative to that across the other of said areas.

18. A method according to claim 12 wherein the effective zeta potential of one of said areas of one of said walls is difierent from that of the opposed area of the other of said walls and wherein said step of adjusting the relative electroosmotic contributions of said areas comprises adjusting the efiective zeta potentials of the remaining opposed areas of said walls to be equal to and opposite in sense to those of said first mentioned areas.

19. A method according to claim 18 wherein said step of adjusting the effective zeta potentials of the remaining opposed areas of said walls comprises:

providing said remaining opposed areas of said walls with different effective zeta potentials which are opposite in sense to the difference in eifective zeta potentials of said one areas of said walls; and adjusting the voltage gradient across said remaining areas relative to that across said one of said areas.

20. In a continuous free flow electrophoresis apparatus having a thin curtain of liquid carrier medium which flows in an electrophoresis space between a pair of spaced walls, the improvement wherein an asymmetry in one portion of said apparatus caused by a difierence in zeta potential between said spaced walls is compensated for by an asymmetry of opposed sense in another portion of said apparatus.

21. In a continuous free flow electrophoresis apparatus according to claim 20, the improvement wherein said compensation is achieved by varying the ratio of the voltage gradients across said portions of said apparatus.

22. Ina continuous free flow electsophoresis apparatus according to claim 2, the improvement wherein said compensation is achieved by varying the ratio of the heights of said pontions of said apparatus.

References Cited UNITED STATES PATENTS 2,555,487 6/1951 Haugaard et al. 204-299 X 3,563,872 2/19'71 Huebner 204299 X JOHN H. MACK, Primary Examiner A. C. PRESCO IT, Assistant Examiner US. Cl. X.R. 204-480 R, 299 

